The Braiding Structure and Duality of the Category of Left–Left BiHom–Yetter–Drinfeld Modules

Abstract

Let (H,μH,ΔH,αH,βH,ψH,ωH,SH) be a BiHom–Hopf algebra. First, we provide a non-trivial example of a left–left BiHom–Yetter–Drinfeld module and show that the category HHBHYD is a braided monoidal category. We also study the connection between the category HHBHYD and the category HM of the left co-modules over a coquasitriangular BiHom–bialgebra (H,σ). Secondly, we prove that the category of finitely generated projective left–left BiHom–Yetter–Drinfeld modules is closed for left and right duality.